← etc / Encyclopedia of Triangle Centers

X₈₈₉¶

INTERSECTION OF LINES X₉₉X_898 AND X₁₉₀X_649

X₈₈₉ (INTERSECTION OF LINES X₉₉X_898 AND X₁₉₀X_649) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_889 = INTERSECTION OF LINES X_99X_898 AND X_190X_649."""

        from __future__ import annotations

        from pathlib import Path

        import sympy.geometry as spg
        from geometor.model import Model

        from geometor.etc.ops import (
            central_line,
            construct_baseline_triangle,
            create_model,
            eval_barycentric_point,
            eval_trilinear_point,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00889(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_889 = INTERSECTION OF LINES X_99X_898 AND X_190X_649 on reference triangle ABC."""
            X_889 = eval_barycentric_point(model, A, B, C, 'b*c/((b - c)*(a*b + a*c - 2*b*c))', ID="X_889", classes=["selected", "target"])
            X_190 = eval_trilinear_point(model, A, B, C, 'b*c/(b - c)', ID="X_190", classes=["center", "incident"])
            X_649 = eval_trilinear_point(model, A, B, C, 'a*(b - c)', ID="X_649", classes=["center", "incident"])
            central_line(model, X_190, X_649, 190, 649, incident=True)
            X_513 = eval_trilinear_point(model, A, B, C, 'b - c', ID="X_513", classes=["center", "incident"])
            X_668 = eval_trilinear_point(model, A, B, C, '1/(a**(2)*(b - c))', ID="X_668", classes=["center", "incident"])
            central_line(model, X_513, X_668, 513, 668, incident=True)
            X_99 = eval_trilinear_point(model, A, B, C, 'b*c/(b**(2) - c**(2))', ID="X_99", classes=["center", "incident"])
            X_898 = eval_trilinear_point(model, A, B, C, '1/((b - c)*(2*b*c - a*b - a*c))', ID="X_898", classes=["center", "incident"])
            central_line(model, X_99, X_898, 99, 898, incident=True)
            return promote_point_to_top(model, X_889)


        def build_model(
            sides: tuple[float, float, float] = (5.0, 6.0, 7.0),
            show_guides: bool = False,
        ) -> Model:
            """Build a `geometor.model.Model` for X_889 on the given reference triangle."""
            model = create_model('X_889 = INTERSECTION OF LINES X_99X_898 AND X_190X_649')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00889(model, A, B, C)
            return model


        if __name__ == "__main__":
            here = Path(__file__).resolve().parent
            model_acute = build_model((5.0, 6.0, 7.0))
            model_acute.save(str(here / "x-00889.json"))
            write_center_svg(
                model_acute,
                here / "x-00889.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X889¶

X₈₈₉¶